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# A research team is to consist of 3 scientists from Company A

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A research team is to consist of 3 scientists from Company A [#permalink]  29 Jul 2020, 11:04
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Question Stats:

83% (00:44) correct 16% (01:11) wrong based on 6 sessions
A research team is to consist of 3 scientists from Company A and 3 scientists from Company B. If the pool of available scientists from Company A is 5 and the pool of available scientists from Company B is 4 scientists, how many different research teams are possible?

(A) 84
(B) 40
(C) 30
(D) 20
(E) 12

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: A research team is to consist of 3 scientists from Company A [#permalink]  29 Jul 2020, 11:16
Expert's post
Carcass wrote:
A research team is to consist of 3 scientists from Company A and 3 scientists from Company B. If the pool of available scientists from Company A is 5 and the pool of available scientists from Company B is 4 scientists, how many different research teams are possible?

(A) 84
(B) 40
(C) 30
(D) 20
(E) 12

Kudos for the right answer and explanation

Take the task of seating the 6 scientists and break it into stages.

Stage 1: Select 3 scientists from Company A
Since the order in which we select the scientists does not matter, we can use combinations.
We can select 3 scientists from the 5 scientists in pool Company A in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways

Stage 2: Select 3 scientists from Company B
Once again, we can use combinations.
We can select 3 scientists from the 5 scientists in pool Company B in 4C3 ways (4 ways)
So, we can complete stage 2 in 4 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus curate the research team) in (10)(4) ways (= 40 ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

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Re: A research team is to consist of 3 scientists from Company A   [#permalink] 29 Jul 2020, 11:16
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